The article investigates various mechanical phenomena by means of mathematical methods. During the research, transcendental equations were created. These equations describe some mechanical phenomena and objects. It is known that transcendental equations are not solved analytically. Therefore, optimal methods for solving these equations have been developed. In this paper, graphic and computer methods are chosen as effective ways to solve transcendental equations. Numerical methods were used to find the root of the equations with a certain accuracy.

The numerical methods used were the method of gradual approximation, iterative method, half division and chord methods.  Several equations have been solved using computer programs. These programs are created in Python and MathCAD environments. In the process of performing the examples discussed in the article, students form a system of knowledge about the deep connection between mechanics, mathematics and computer science.